Flow in powders: From discrete avalanches to continuous regime

Segregation patterns in three-dimensional granular flows

Flow of size-bidisperse particle mixtures in a spherical tumbler rotating alternately about two perpendicular axes produces segregation patterns that track the location of nonmixing islands predicted by a dynamical systems approach. To better understand the paradoxical accumulation of large particles in regions defined by barriers to transport, we perform discrete element method (DEM) simulations to visualize the three-dimensional structure of the segregation patterns and track individual particles. Our DEM simulations and modeling results indicate that segregation pattern formation in the biaxial spherical tumbler is due to the interaction of size-driven radial segregation with the weak spanwise component of the advective surface flow. Specifically, we find that after large particles segregate to the surface, slow axial drift in the flowing layer, which is inherent to spherical tumblers, is sufficient to drive large particles across nominal transport barriers and into nonmixing islands predicted by an advective flow model in the absence of axial drift. Axial drift alters the periodic dynamics of nonmixing islands, turning them into "sinks" where large particles accumulate even in the presence of collisional diffusion. Overall, our results indicate that weak perturbation of chaotic flow has the potential to alter key dynamical system features (e.g., transport barriers), which ultimately can result in unexpected physical phenomena.

Continuous to intermittent flows in growing granular heaps

If a granular material is poured from above on a horizontal surface between two parallel, vertical plates, a sand heap grows in time. For small piles, the grains flow smoothly downhill, but after a critical pile size X_{c}, the flow becomes intermittent: sudden avalanches slide downhill from the apex to the base, followed by an "uphill front" that slowly climbs up, until a new downhill avalanche interrupts the process. By means of experiments, controlling the distance between the apex of the sandpile and the container feeding it from above, we show that X_{c} grows linearly with the input flux, but scales as the square root of the feeding height. We explain these facts from a phenomenological model based on the experimental observation that the flowing granular phase forms a "wedge" on top of the static one, differently from the case of stationary heaps. Moreover, we demonstrate that our controlled experiments allow to predict the value of X_{c} for the common situation in which the feeding height decreases as the pile increases in size.

Clogging and avalanches in quasi-two-dimensional emulsion hopper flow

We experimentally and computationally study the flow of a quasi-two-dimensional emulsion through a constricting hopper shape. Our area fractions are above jamming such that the droplets are always in contact with one another and are in many cases highly deformed. At the lowest flow rates, the droplets often clog and thus exit the hopper via intermittent avalanches. At the highest flow rates, the droplets exit continuously. The transition between these two types of behaviors is a fairly smooth function of the mean strain rate. The avalanches are characterized by a power-law distribution of the time interval between droplets exiting the hopper, with long intervals between the avalanches. Our computational studies reproduce the experimental observations by adding a flexible compliance to the system (in other words, a finite stiffness of the sample chamber). The compliance results in continuous flow at high flow rates, and allows the system to clog at low flow rates leading to avalanches. The computational results suggest that the interplay of the flow rate and compliance controls the presence or absence of the avalanches.

Impact of Powder Properties on the Rheological Behavior of Excipients

With the emergence of quality by design in the pharmaceutical industry, it becomes imperative to gain a deeper mechanistic understanding of factors impacting the flow of a formulation into tableting dies. Many flow characterization techniques are present, but so far only a few have shown to mimic the die filling process successfully. One of the challenges in mimicking the die filling process is the impact of rheological powder behavior as a result of differences in flow field in the feeding frame. In the current study, the rheological behavior was investigated for a wide range of excipients with a wide range of material properties. A new parameter for rheological behavior was introduced, which is a measure for the change in dynamic cohesive index upon changes in flow field. Particle size distribution was identified as a main contributing factor to the rheological behavior of powders. The presence of fines between larger particles turned out to reduce the rheological index, which the authors explain by improved particle separation at more dynamic flow fields. This study also revealed that obtained insights on rheological behavior can be used to optimize agitator settings in a tableting machine.

Triggering avalanches by transverse perturbations in a rotating drum

We study the role of small-scale perturbations in the onset of avalanches in a rotating drum in the stick-slip regime. By vibrating the system along the axis of rotation with an amplitude orders of magnitude smaller than the particles’ diameter, we found that the order parameter that properly describes the system is the kinetic energy. We also show that, for high enough frequencies, the onset of the avalanche is determined by the amplitude of the oscillation, contrary to previous studies that showed that either acceleration or velocity was the governing parameter. Finally, we present a theoretical model that explains the transition between the continuous and discrete avalanche regimes as a supercritical Hopf bifurcation.

Experimental study of particle shape dependence of avalanches inside a rotating drum

We investigate the avalanches of spherical and non-spherical granular particles inside half-filled rotating drums. The time series of the center of gravity of the particle assemblies are obtained via image analysis and their single-sided amplitude (SSA) spectra are analyzed. The spectra features of this new indicator turn out to be characteristic for the avalanches, in terms of the existence of peaks in the low-frequency range and the decay rate of high frequency components. The SSA spectrum has a peak for the packings of non-spherical particles but not for the spherical particles. The high frequency part is characterized by a power law decay 1/ f a (a > 0) . A 1/ f -decay is found only for the spherical particles. For the packings of cornered particles, the exponents significantly deviate from a = 1. As 1/ f spectra are often associated with self-organized criticality and therefore a scale invariance of the dynamics, we may conclude that there is no scale-invariant structure for granular avalanches. Considering the small number of particles and the regularity of convex particle shapes being used, the spectral features revealed in this study could be utilized for validating particle simulations.

Sidewall-friction-driven ordering transition in granular channel flows: Implications for granular rheology

We report a transition from a disordered state to an ordered state in the flow of nearly monodisperse granular matter flowing in an inclined channel with planar slide walls and a bumpy base, using discrete element method simulations. For low particle-sidewall friction coefficients, the flowing particles are disordered, however, for high sidewall friction, an ordered state is obtained, characterized by a layering of the particles and hexagonal packing of the particles in each layer. The extent of ordering, quantified by the local bond-orientational order parameter, varies in the cross section of the channel, with the highest ordering near the sidewalls. The flow transition significantly affects the local rheology-the effective friction coefficient is lower, and the packing fraction is higher, in the ordered state compared to the disordered state. A simple model, incorporating the extent of local ordering, is shown to describe the rheology of the system.

Clustering and velocity distributions in granular gases cooling by solid friction

We present large-scale molecular dynamics simulations to study the free evolution of granular gases. Initially, the density of particles is homogeneous and the velocity follows a Maxwell-Boltzmann (MB) distribution. The system cools down due to solid friction between the granular particles. The density remains homogeneous, and the velocity distribution remains MB at early times, while the kinetic energy of the system decays with time. However, fluctuations in the density and velocity fields grow, and the system evolves via formation of clusters in the density field and the local ordering of velocity field, consistent with the onset of plug flow. This is accompanied by a transition of the velocity distribution function from MB to non-MB behavior. We used equal-time correlation functions and structure factors of the density and velocity fields to study the morphology of clustering. From the correlation functions, we obtain the cluster size, L, as a function of time, t. We show that it exhibits power law growth with L(t)∼t^{1/3}.

Influence of particle surface roughness on creeping granular motion

A core is formed at the center of a quasi-two-dimensional rotating drum filled more than half with granular material. The core rotates slightly faster than the drum (precession) and decreases in radius over time (erosion) due to the granular creeping motion that occurs below the freely flowing layer. This paper focuses on the effect of the surface roughness of particles on core dynamics, core precession, and core erosion. Two different surface roughness of glass particles having the same diameter were used in the experiments. The surface structures of the particles were quantitatively compared by measuring the coefficients of friction and using a simple image contrast method. The experiments were performed with five different filling levels in a 50-cm-diameter rotating drum. According to the results, core precession and core erosion are both dependent on the particle surface roughness. Core precession becomes weaker and erosion becomes stronger when using particles having a rough surface in the experiments. To explain the physics of core dynamics, the particles' surface roughness effect on the freely flowing layer and the creeping motion region were also investigated. The granular bed velocity field, maximum flowing layer depth δ, shear rate in the flowing layer γ[over ̇], and the creeping region decay constant y_{0} were also calculated in this paper. The effect of the particles' surface roughness on these physical variables well illustrates the physics of core dynamics and creeping granular motion.

Dissipation of Energy by Dry Granular Matter in a Rotating Cylinder

We study experimentally the dissipation of energy in a rotating cylinder which is partially filled by granular material. We consider the range of angular velocity corresponding to continous and stationary flow of the granulate. In this regime, the stationary state depends on the angular velocity and on the filling mass. For a wide interval of filling levels we find a universal behavior of the driving torque required to sustain the stationary state as a function of the angular velocity. The result may be of relevance to industrial applications, e.g. to understand the power consumption of ball mills or rotary kilns and also for damping applications where mechanical energy has to be dissipated in a controlled way.

Granular flow regimes in rotating drums from depth-integrated theory

Granular flows in rotating drums transition between two regimes characterized by straight and curved free surfaces. Here we predict this behavior using a depth-integrated theory applicable to general eroding flows. Closure is achieved by a local μ(I) rheology and an equation for kinetic energy. Spanning the transition, the theory yields relations for all flow properties in terms of a single dimensionless rotation rate. In accord with experiments, distinct scaling laws are obtained for slow and fast rates, dominated respectively by local energy dissipation and longitudinal energy transfer.

Grains unchained: local fluidization of a granular packing by focused ultrasound

We report experimental results on the dynamics of a granular packing submitted to high-intensity focused ultrasound. Acoustic radiation pressure is shown to remotely induce local rearrangements within a pile as well as global motion around the focal spot in an initially jammed system. We demonstrate that this fluidization process is intermittent for a range of acoustic pressures and hysteretic when the pressure is cycled. Such a first-order-like unjamming transition is reproduced in numerical simulations in which the acoustic pressure field is modeled by a localized external force. Further analysis of the simulated packings suggests that in the intermittent regime unjamming is not associated with any noticeable prior structural signature. A simple two-state model based on effective temperatures is proposed to account for these findings.

Numerical analysis of granular flows in a silo bed on flow regime characterization

The flow characteristics of a gravity-driven dense granular flow in a granular bed with a contracted drainage orifice are studied by using discrete element method and quantitative analysis. Three values of discharging rates, ranging from fast to slow dense flows, are investigated. Time variations and derivatives of mean forces and velocities, as well as their respective correlations, are analyzed to quantitatively depict the characteristics of granular flow as well as flow regime categorization. The auto-correlation functions, as well as their Fourier spectrums, are utilized to characterize the differences between the mechanisms of slow and fast granular flows. Finally, it is suggested that the flow regimes of slow and fast flows can be characterized by the kinetic and kinematic flow properties of particles.

Ringlike spin segregation of binary mixtures in a high-velocity rotating drum

This study presents molecular dynamics simulations on the segregation of binary mixtures in a high-velocity rotating drum. Depending on the ratio between the particle radius and density, similarities to the Brazil-nut effect and its reverse form are shown in the ringlike spin segregation patterns in radial direction. The smaller and heavier particles accumulated toward the drum wall, whereas the bigger and lighter particles accumulated toward the drum center. The effects of particle radius and density on the segregation states were quantified and the phase diagram of segregation in the ρ(b)/ρ(s) - r(b)/r(s) space was plotted. The observed phenomena can be explained by the combined percolation and the buoyancy effects.

Flow of magnetized grains in a rotating drum

We have experimentally investigated the influence of a magnetic interaction between the grains on the flow of a granular material in a rotating drum. The magnetic cohesion is induced by applying a homogeneous external magnetic field B oriented either parallel or perpendicular to the gravity g. The drum rotating speed has been selected to obtain a continuous flow when the magnetic field is switched off. We show that, for both magnetic field orientations, the cohesion is able to induce a transition between the continuous flow regime to the discrete avalanche regime. The avalanche dynamics is periodic when B⊥g and irregular when B∥g. Moreover, the maximal angle of stability θ(m) increases strongly with the cohesion strength and could be higher than 90° when B⊥g. A toy model based on the stability of a magnetic block on a magnetic inclined plane is proposed to explain this behavior.

Chaotic mixing via streamline jumping in quasi-two-dimensional tumbled granular flows

We study, numerically and analytically, the singular limit of a vanishing flowing layer in tumbled granular flows in quasi-two-dimensional rotating containers. The limiting behavior is found to be identical under the two versions of the kinematic continuum model of such flows, and the transition to the limiting dynamics is analyzed in detail. In particular, we formulate the no-shear-layer dynamical system as a piecewise isometry. It is shown how such a discontinuous map, through the concordant mechanism of streamline jumping, leads to the physical mixing of granular matter. The dependence of the dynamics of Lagrangian particle trajectories on the tumbler fill fraction is also established through Poincaré sections, and, in the special case of a half-full tumbler, chaotic behavior is shown to disappear completely in the singular limit. At other fill levels, stretching in the sense of shear strain is replaced by spreading due to streamline jumping. Finally, we use finite-time Lyapunov exponents to establish the manifold structure and understand "how chaotic" the limiting piecewise isometry is.

Streamline jumping: a mixing mechanism

We study a singular limit of tumbled granular flows in quasi-two-dimensional rotating drums, demonstrating that the limiting dynamical system, as the shear layer vanishes, belongs to a class of discrete discontinuous mappings called piecewise isometries. In doing so, we identify a mechanism of mixing, in the absence of the usual streamline crossing mediated by the flowing layer. By considering the exceptional case of a 50% full square tumbler, this mechanism (streamline jumping) is related to the horizontal motion of the free surface of the flow in non-half-full tumblers. The limiting dynamics are quite complex, if not (technically) chaotic.

Granular coarsening: phase space and evolution analogies

Various aspects of axial banding of size-varying bidisperse granular mixtures in cylindrical tumblers have been documented repeatedly over a decade or so, but the dependence of surface band formation on the relative concentration of particles and rotation rate has not been thoroughly examined. Coarsening patterns analogous to nucleation and spinodal decomposition occur as the relative concentration of small and large particles and the rotation rate of the tumbler are varied. A phase diagram with a portion analogous to a miscibility gap can be constructed from the space-time plots. A dynamic scaling approach similar to that for reacting lamellae can be applied to the coarsening patterns as a result of large bands growing at the expense of neighboring smaller bands.

Crossover transition in flowing granular chains

We report on the dynamical and statistical behavior of flowing collections of granular chains confined two-dimensionally (2D) within a rotating tumbler. Experiments are conducted with systems of chains of fixed length, but various lengths are considered. The dynamics are punctuated by cascades of chains along a free-surface cascades, which drive the development of mixed porous/laminar packing arrangements in bulk. We investigate the conformation of the system, as characterized by the porosity of the flow region occupied by the chains and the mean-square end-to-end distance of the chains during flow. Both of these measures show crossover transitions from a 2D self-avoiding walk to a 2D random walk when the chain length becomes long enough to allow self-contact.

Transition by intermittency in granular matter: from discontinuous avalanches to continuous flow

We investigate, in the rotating drum configuration, the transition from the regime of discontinuous avalanches observed at low angular velocity to the regime of continuous flow observed at higher velocity. Instead of the hysteretic transition reported previously by Rajchenbach [Phys. Rev. Lett. 65, 2221 (1990)], with an apparent bistability of the two flow regimes in a range of drum velocities, we observe intermittency with spontaneous erratic switches from one regime to the other. Both scenarios of transition are recovered by a model dynamic equation for the avalanche flow with two sources of stochasticity: a Langevin noise during the avalanche flow and a distributed maximal stability angle at which avalanches start.